The present invention relates to an imaging system which includes a gradient index lens array to focus light onto an image plane, and more particularly to a gradient index lens array modified so as to increase the depth of focus of the array without any loss of radiometric efficiency. Light transmitters comprising bundled gradient index optical fibers, or rods, are known in the art. U.S. Pat. No. 3,658,407 describes a light conducting rod made of glass or synthetic resin which has a refractive index distribution in a cross section thereof that varies parabolically outward from a center portion thereof. Each rod acts as a focusing lens for light introduced at one end. The rod lenses are produced under the trade name "SELFOC"; the mark is registered in Japan and owned by Nippon Sheet Glass Company, Ltd. Relevant optical characteristics of gradient index lens arrays are described in an article entitled "Optical properties of GRIN fiber lens arrays: dependence on fiber length", by William Lama, Applied Optics, Aug. 1, 1982, Vol. 21, No. 15, pages 2739-2746. This article is hereby incorporated by reference.
These rod lens arrays have found utility in a number of document imaging systems. Typically, an assembly of rods are arranged linearly in a one row or a staggered two row array. The arrays are used as a replacement for conventional optical systems in copiers as disclosed in U.S. Pat. Nos. 3,947,106 and 4,193,679. The arrays are also used in a Raster Input Scanner (RIS) to focus light reflected from a scanned document onto photosensors which electronically capture the scanned image (see, for example, U.S. Pat. No. 4,509,826). The arrays are also used in conjunction with printers which utilize LED print bars as the imager to expose a photoreceptor surface. The gradient index lens array is positioned between the LED print bar and the photoreceptor surface to transmit the light output from the activated LED emitters as focused light spots on the photoreceptor surface. U.S. Pat. No. 4,801,978, for example, shows a printer with a single print bar imager. U.S. Pat. No. 5,166,999 discloses a single pass printer with a plurality of print bars positioned adjacent to the surface of a photoreceptor belt, each print bar having an associated gradient index lens array. This system forms successive registered color images on the surface of a photoreceptor.
For those scanning applications where the lens arrays are focusing light reflected from a document platen, adequate depth of focus (DOF) is a critical concern. For LED print bar systems, adequate DOF at the photoreceptor is also a critical concern. For both types of applications, it is desirable for the DOF of the gradient index lens array to be as large as possible consistent with optimum radiometric efficiency. The DOF of a conventional lens can be increased by increasing the relative aperture or f/# of a conventional lens. FIG. 1A illustrates a prior art imaging lens system. Lens L1 has an exit pupil diameter D.sub.1, and a focal length FL and a depth of focus DOF. The f/# of the FIG. 1A system is the focal length FL divided by the diameter of the exit pupil or, f/#=FL.div.D.sub.1.
It can be shown that two relationships exist for this prior art system. The radiometric speed is inversely proportional to (f/#).sup.2 =(D.div.FL).sup.2 and the DOF is proportional to f/# or (FL.div.D). The DOF of the optical system of FIG. 1A can therefore be increased to that shown in FIG. 1B (DOF') by using a lens L2 with a smaller exit pupil diameter D.sub.2. The focal length FL remains the same for each system. However, by the first relationship above, radiometric speed equals (f/#).sup.2 =(D/FL).sup.2, and there is a loss in radiometric speed for the system of FIG. 1B. It therefore follows that radiometric speed and DOF are diametrically opposed. DOF can be increased (by reducing the relative aperture) but only at a significant loss in radiometric speed. Likewise, radiometric speed can be increased but only with a reduction in DOF.
For the case of a gradient index lens array imaging system, it can be shown that the radiometric efficiency is proportional to the quantity (n.sub.o .sqroot.A.times.R).sup.2 where n.sub.o is the axial refractive index of the optical rods, .sqroot.A is a lens gradient index constant and R is the radius of the individual rods. The DOF is inversely proportional to n.sub.o .sqroot.AR; e.g. DOF.varies.1.div.n.sub.o .sqroot.AR.
It is a desirable object, heretofore unrealized, to increase the DOF of a gradient index lens array while maintaining desired radiometric efficiency. The present invention sets forth a method for accomplishing this by changing the asymmetric effective aperture (exit pupil) of a conventional gradient index lens array into a general circularly symmetrical effective aperture by techniques described in detail below. These techniques, as will be seen, reduce the value of the quantity n.sub.o .sqroot.AR to maintain a desired DOF while trading off against initially higher radiometric efficiencies. More particularly, the invention relates to an imaging system. An imaging system for focusing light from an object plane onto an image plane, said imaging system including a gradient index lens array comprising gradient index optical rods combined into at least two linear rows, each of said optical rods having an entrance pupil and an exit pupil and wherein a plurality of adjoining rods contribute to the exposure of a single point at the image plane, said plurality of rods having an effective exit pupil which has a generally circularly symmetric shape.